Algebra

posted by .

Which of the following statements from Euclidean geometry is also true of spherical geometry?

A) A line has infinite length.
B) Two intersecting lines divide the plane into four regions.
C) Two perpendicular lines create four right angles.
D)The intersection of two lines creates four angles.
Im realy having trouble on this quesiton & I need some help:) thankyou!

  • Algebra -

    Think of great circles on a sphere. Those correspond to straight lines in a plane. An arc of a great circle is the shortest distance between two points, measured along the surface of the sphere. A great circle is one whose diameter is the same as the diameter of the sphere.

    not A: On a sphere, a great circle does not have infinite length.

    not B: Anything pertaining to a plane has no relevance on a sphere.

    not C: Two perpendicular great circles intersect twice. Think of the equator and a meridian. At each intersection there are 4 right angles.

    D: This is true. Although as in C, two "lines" on a sphere always intersect twice.

    By the way, that means that in spherical geometry, there are no parallel lines!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. maths geometry

    Find and write down a proof that the product of the gradients of two perpendicular lines is -1 Use trigonometry. Let the slope of a line from A to B be m1. Let the slope of a perpendicular line from A to C be m2. The tangent (or slope) …
  2. Geometry

    I don't get these questions Is there exactly one plane containing two non intersecting lines?
  3. Geometry

    For each property listed from plane Euclidean geometry, write a corresponding statement for non-Euclidean spherical geometry. A line segment is the shortest path between two points Hey guys I want to know how to do this and can you …
  4. Geometry

    Which of the following statements from Euclidean geometry is also true of spherical geometry?
  5. geometry

    Martin drew a pair of perpendicular lines and a pair of parallel lines. Which of these statements best compares the pairs of perpendicular and parallel lines?
  6. Geometry

    Which statement from Euclidean geometry is also true in spherical geometry?
  7. geometry

    When constructing parallel and perpendicular lines, how are the steps similar?
  8. Math

    1. Write the following reversible as a biconditional: If two perpendicular lines intersect, they form four 90* angles. A) Two intersecting lines are perpendicular if and only if they form four 90* angles. B) Two intersecting, perpendicular …
  9. geometry

    Create a wrapping paper design that includes at least four of the following constructions: a bisected angle a perpendicular line drawn from a point not on a line to a line a perpendicular line drawn through a given point on a given …
  10. Geometry

    write the following reversible statement as a biconditional: If two perpendicular lines intersect, they form four 90 degree angles. -Two intersecting lines are perpendicular if and only if they form four angles. -Two intersecting, …

More Similar Questions